Step 1: Understanding the composition of the Telangana Legislative Council.
In the Telangana Legislative Council, members are elected through different categories, including teachers and graduates. The portion of members elected by teachers is defined by the state legislature.
Step 2: Correct answer explanation.
According to the Telangana Legislative Council Act, \( \frac{1}{12} \) of the total members are elected by teachers. This is the proportion of members representing teachers in the council.
Step 3: Conclusion.
Therefore, the correct answer is \( \frac{1}{12} \).
Final Answer: \( \frac{1}{12} \) th.